1. Field of the Invention
This invention relates generally to a method and system for controlling the solar torque on a spacecraft, and, more particularly, to a method and system for controlling the solar torque on a spacecraft using a directionally reflecting, emitting, absorbing, and transmitting surface.
2. Discussion of the Related Art
When a spacecraft is in space, a variety of environmental disturbances, including solar pressure, gravity-gradient, magnetic and aerodynamic effects, act on the spacecraft producing forces and torques. These forces and torques vary depending on the spacecraft's orbital altitude. If the spacecraft is in a low Earth orbit (LEO), the forces and torques other than solar pressure are typically dominant because they vary inversely with orbital radius. If the spacecraft is in a high altitude orbit, such as a geosyncronous Earth orbit (GEO), the dominant disturbance is solar pressure. This discussion deals with solar torque. The article, Harris, Christian M. et al, “Effect of Thermal Radiation Torques on the TDRS Spacecraft,” American Institute of Aeronautics and Astronautics, Inc., 1990, pgs. 1602-1614 also provides a discussion of solar torque on a spacecraft.
Various spacecraft, such as the next generation space telescope (NGST), the terrestrial planet finder (TPF) and the planet imager (PI), require sun shades that can be extremely large in order to protect cryogenic instruments mounted on the spacecraft. These large sunshades are typically opaque and receive large amounts of incident solar radiation, and thus may increase the solar torque on the spacecraft. Spacecraft systems of this type are typically designed to point off-angle from the sun, usually within a 45° “anti-sun” conical region. If the center of pressure (CP) of the incident solar radiation is co-incident with the spacecraft center of mass (CM), then little or no solar torque is produced. However, typical spacecraft designs preclude co-locating the center of pressure and the center of mass because of mission payload configuration constraints.
FIG. 1 is a simple schematic of a spacecraft 10, such as the TPF or NGST, used to illustrate how solar pressure produces spacecraft disturbance torque. The spacecraft 10 includes a bus 12 positioned on one side of a thermal shield assembly 14, and sensor optics 16 positioned on the opposite side of the thermal shield assembly 14. The bus 12 houses the spacecraft avionics subsystems and is typically on the “sun side” of the assembly 14. The thermal shield assembly 14 includes a multi-layer insulation (MLI) 18 on the bus side of the assembly 14, and a series of angled specular shields 20 that act to reflect light and heat away from the sensor optics 16. In one design, the optics 16 are on the order of two meters, and the shields 20 are on the order of 10 meters.
Based on the spacecraft schematic shown in FIG. 1, a simplified schematic of the center of mass 24 and the center of pressure 26 of the spacecraft 10 relative to a solar shield 28 as shown in FIG. 2. The solar shield 28 represents the thermal shield assembly 14. Typically, the spacecraft center of mass 24 is on the bus side of the thermal shield 28, and the center of pressure 26 is at the geometric center of the thermal shield 28.
FIG. 3 utilizes the schematic shown in FIG. 2 to depict the forces generated by solar radiation pressure that impinges normal to the shield 28 and the resultant thermal radiation from the shield 28. Incident photons 30 can be either absorbed, specularly reflected at 32 in a mirror like manner, or can be reflected in a diffuse manner at 34, sometimes referred to as a Lambertian distribution. The absorbed energy must be emitted as thermal radiation energy with the bulk of the thermal emission occurring from the sun side due to the insulation effectiveness. This emitted thermal energy also typically has a Lambertian energy distribution 35. The resultant force vector due to the reradiated thermal energy is shown at 43. Thus, there are four force vectors caused by the impinging photons 30, including a force vector 40 from the absorption of the incident photons 30, a force vector 38 from the specularly reflected photons, and force vector 42 from the diffusely reflected photons and the force vector 43 from thermal radiation. For reference, a highly specular surface produces twice the reaction force (due to solar radiation pressure) generated by a highly absorptive surface. The combination of the force vectors 38-43 gives an effective force vector 44. For this depiction, the sunlight is aligned along an axis running through the CM 24 and the CP 26, where the effective force vector 44 is along this axis. Therefore, the resultant force vectors are the same at both sides of the shield 28, resulting in no net torque being imposed on the spacecraft 10.
For typical sunshield designs, most of the incident light energy is reflected or absorbed and re-emitted from the shield 28 at the side facing the sun. The thermal insulating nature of the thermal shield 28 reduces heat leakage to one or two percent of the total incident front side energy. Therefore, backside thermal radiation is negligible due to the effectiveness of the thermal shield 28. In a situation where the CM 24 and the CP 26 are co-aligned relative to the direction of the incident sunlight, there is no net induced torque on the spacecraft 10.
The force on a surface due to photon absorption, i.e., the force due to solar radiation pressure, is given by:Fabsorbed=SA/c,  (1) where Fabsorbed is the absorption force, S is solar flux (power per unit area), A is the projected area, and c is the speed of light. For a specular surface, the angle of incidence of the impinging photons equals the angle of reflection of the reflected photons, resulting in a force opposite to the surface normal vector direction. Thus, when the incident surface is totally specularly reflective, and the surface is normal to the sun vector, the specular reflection force (Freflection specular) is given by Freflection specular=2SA/c. A diffusely reflective surface, i.e., Lambertian distribution, produces a force given by:Freflection diffuse=2SA/3c.  (2) 
Emitted photons also result in forces opposite to the direction of travel of the emitted photon. The article, Harris, Christian, M. et al., “Effect of Thermal Radiation Torques on the TDRS Spacecraft,” provides the following equation for modeling the thermal radiation force:                                           F                          thermal              ⁢                                                           ⁢              radiation                                =                                    2              3                        ⁢                                          Q                                  thermal                  ⁢                                                                           ⁢                  radiation                                            C                        ⁢            A                          ,                            (        3        )            where Qthermal radiation=σ εT4 is the thermal radiation emissive power per unit area, and is given by the Stefan-Boltzmann law.
For most spacecraft functions, the pointing direction of the optics, and thus the pointing direction of the entire spacecraft, will be in such a direction that the incident solar radiation is angled relative to the axis through the CM 24 and the CP 26. FIG. 4 is a representation of the schematic shown in FIG. 3 where the shield 28 is angled relative to the incident solar radiation, and the CM 24 is thus tilted to the left. Each of the force vectors generated by the incident, reflected and radiated photons identified in FIG. 3 are shown in FIG. 4. However, the direction of the reflected and emitted radiation is different, and therefore the effective force vector 44 is not aligned with the CM 24 and CP 26 axis. Because the effective force vector 44 acts through the CP 26 and is not aligned along the axis between the CM 24 and CP 26, a torque is created about the CM 24 identified by a moment 46 in the clockwise direction.
The net torque T produced by a single surface about the spacecraft 10 body axes is then:T=LCP-CM×(Fabsorbed radiation+Freflected radiation+Femitted radiation)  (4) where LCP-CM is the position vector from the center of mass 24 to the surface center of pressure 26. For the spacecraft, the total magnitude of the generated torque T can be determined by an area integration of the cross-product of the local force vector and the respective CP/CM moment arm of the localized surface area elements, dA, given as:                     T        =                                            ∫              A                        ⁢                                                            L                  →                                ⁡                                  (                                      θ                    ,                    r                    ,                    ϕ                                    )                                            ⁢              x              ⁢                              ⅆ                                  F                  →                                                              =                                    ∫              A                        ⁢                                                            L                  →                                ⁡                                  (                                      θ                    ,                    r                    ,                    ϕ                                    )                                            ⁢              x              ⁢                                                f                  →                                ⁡                                  (                                      θ                    ,                    r                    ,                    ϕ                    ,                                          Φ                      s                                                        )                                            ⁢                              ⅆ                A                                                                        (        5        )            where θ, r, φ are the spherical coordinates in body-axes and Φs is the angle of incident sun.
Various techniques are known in the art to compensate for solar torques. One of these includes employing torque compensating reaction wheels (one wheel is provided for each spacecraft body axis) that provide spacecraft attitude control. As the solar torque acts on the spacecraft, one or more of the wheels is accelerated to compensate for the solar pressure disturbance torque resulting in wheel momentum accumulation. Periodically, it is necessary to unload momentum from the reaction wheels to prevent saturation.
Suitable momentum unloading compensation can be performed by magnetic torquers if the spacecraft is in a low Earth orbit, where the Earth's magnetic field strength is sufficiently large to produce appreciable magnetic torques. In this situation, a magnetic dipole is generated using onboard magnetic torque rods that interact with the Earth's magnetic field to produce a torque. However, as the spacecraft orbital altitude gets farther from the Earth, the Earth's magnetic field strength reduces rapidly (proportional to 1/R3, where R=orbital radius), thus reducing the ability to provide this type of momentum unloading. For high orbit altitudes where momentum unloading cannot be provided by Earth's magnetic field, typically the spacecraft thrusters are used to provide momentum unloading of the wheels. However, spacecraft weight is an important design consideration, and therefore, thruster firings should be minimized in order to reduce on board propellant requirements.
Some spacecraft designs employ appendages (e.g., solar sails) to align the spacecraft center of pressure with the spacecraft center of mass to reduce solar torques. Other possible approaches for mitigating solar torque include active devices such as moveable fins or electrochromic surfaces. However, these types of devices are typically expensive and heavy, and are generally unproven and have a limited reliability. A simple, low cost approach to mitigating the effects of solar torque on spacecraft which have large surface areas, is thus needed.
When a spacecraft failure occurs, the onboard computers typically direct the spacecraft to a sun-pointing safe-hold attitude. Sun-pointing provides power with proper solar array orientation, and by design provides a benign or low torque, stable thermal environment. The spacecraft can typically remain in this orientation indefinitely while ground based diagnostics examine telemetry and implement failure work arounds. Typically, reaction wheels are shut down, and the spacecraft thrusters are used to orient the spacecraft to maintain the sun-pointing direction.
Various systems are known in the art for accumulating and unloading angular momentum, as well as for directing the spacecraft to the sun-pointing direction. However, these systems are typically complicated and expensive. What is also needed is a passive method of reducing solar induced torque and achieving and maintaining sun-pointing.